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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    <a name="line.17"></a>
<FONT color="green">018</FONT>    package org.apache.commons.math3.ode.nonstiff;<a name="line.18"></a>
<FONT color="green">019</FONT>    <a name="line.19"></a>
<FONT color="green">020</FONT>    import org.apache.commons.math3.analysis.solvers.UnivariateSolver;<a name="line.20"></a>
<FONT color="green">021</FONT>    import org.apache.commons.math3.exception.DimensionMismatchException;<a name="line.21"></a>
<FONT color="green">022</FONT>    import org.apache.commons.math3.exception.MaxCountExceededException;<a name="line.22"></a>
<FONT color="green">023</FONT>    import org.apache.commons.math3.exception.NoBracketingException;<a name="line.23"></a>
<FONT color="green">024</FONT>    import org.apache.commons.math3.exception.NumberIsTooSmallException;<a name="line.24"></a>
<FONT color="green">025</FONT>    import org.apache.commons.math3.ode.ExpandableStatefulODE;<a name="line.25"></a>
<FONT color="green">026</FONT>    import org.apache.commons.math3.ode.events.EventHandler;<a name="line.26"></a>
<FONT color="green">027</FONT>    import org.apache.commons.math3.ode.sampling.AbstractStepInterpolator;<a name="line.27"></a>
<FONT color="green">028</FONT>    import org.apache.commons.math3.ode.sampling.StepHandler;<a name="line.28"></a>
<FONT color="green">029</FONT>    import org.apache.commons.math3.util.FastMath;<a name="line.29"></a>
<FONT color="green">030</FONT>    <a name="line.30"></a>
<FONT color="green">031</FONT>    /**<a name="line.31"></a>
<FONT color="green">032</FONT>     * This class implements a Gragg-Bulirsch-Stoer integrator for<a name="line.32"></a>
<FONT color="green">033</FONT>     * Ordinary Differential Equations.<a name="line.33"></a>
<FONT color="green">034</FONT>     *<a name="line.34"></a>
<FONT color="green">035</FONT>     * &lt;p&gt;The Gragg-Bulirsch-Stoer algorithm is one of the most efficient<a name="line.35"></a>
<FONT color="green">036</FONT>     * ones currently available for smooth problems. It uses Richardson<a name="line.36"></a>
<FONT color="green">037</FONT>     * extrapolation to estimate what would be the solution if the step<a name="line.37"></a>
<FONT color="green">038</FONT>     * size could be decreased down to zero.&lt;/p&gt;<a name="line.38"></a>
<FONT color="green">039</FONT>     *<a name="line.39"></a>
<FONT color="green">040</FONT>     * &lt;p&gt;<a name="line.40"></a>
<FONT color="green">041</FONT>     * This method changes both the step size and the order during<a name="line.41"></a>
<FONT color="green">042</FONT>     * integration, in order to minimize computation cost. It is<a name="line.42"></a>
<FONT color="green">043</FONT>     * particularly well suited when a very high precision is needed. The<a name="line.43"></a>
<FONT color="green">044</FONT>     * limit where this method becomes more efficient than high-order<a name="line.44"></a>
<FONT color="green">045</FONT>     * embedded Runge-Kutta methods like {@link DormandPrince853Integrator<a name="line.45"></a>
<FONT color="green">046</FONT>     * Dormand-Prince 8(5,3)} depends on the problem. Results given in the<a name="line.46"></a>
<FONT color="green">047</FONT>     * Hairer, Norsett and Wanner book show for example that this limit<a name="line.47"></a>
<FONT color="green">048</FONT>     * occurs for accuracy around 1e-6 when integrating Saltzam-Lorenz<a name="line.48"></a>
<FONT color="green">049</FONT>     * equations (the authors note this problem is &lt;i&gt;extremely sensitive<a name="line.49"></a>
<FONT color="green">050</FONT>     * to the errors in the first integration steps&lt;/i&gt;), and around 1e-11<a name="line.50"></a>
<FONT color="green">051</FONT>     * for a two dimensional celestial mechanics problems with seven<a name="line.51"></a>
<FONT color="green">052</FONT>     * bodies (pleiades problem, involving quasi-collisions for which<a name="line.52"></a>
<FONT color="green">053</FONT>     * &lt;i&gt;automatic step size control is essential&lt;/i&gt;).<a name="line.53"></a>
<FONT color="green">054</FONT>     * &lt;/p&gt;<a name="line.54"></a>
<FONT color="green">055</FONT>     *<a name="line.55"></a>
<FONT color="green">056</FONT>     * &lt;p&gt;<a name="line.56"></a>
<FONT color="green">057</FONT>     * This implementation is basically a reimplementation in Java of the<a name="line.57"></a>
<FONT color="green">058</FONT>     * &lt;a<a name="line.58"></a>
<FONT color="green">059</FONT>     * href="http://www.unige.ch/math/folks/hairer/prog/nonstiff/odex.f"&gt;odex&lt;/a&gt;<a name="line.59"></a>
<FONT color="green">060</FONT>     * fortran code by E. Hairer and G. Wanner. The redistribution policy<a name="line.60"></a>
<FONT color="green">061</FONT>     * for this code is available &lt;a<a name="line.61"></a>
<FONT color="green">062</FONT>     * href="http://www.unige.ch/~hairer/prog/licence.txt"&gt;here&lt;/a&gt;, for<a name="line.62"></a>
<FONT color="green">063</FONT>     * convenience, it is reproduced below.&lt;/p&gt;<a name="line.63"></a>
<FONT color="green">064</FONT>     * &lt;/p&gt;<a name="line.64"></a>
<FONT color="green">065</FONT>     *<a name="line.65"></a>
<FONT color="green">066</FONT>     * &lt;table border="0" width="80%" cellpadding="10" align="center" bgcolor="#E0E0E0"&gt;<a name="line.66"></a>
<FONT color="green">067</FONT>     * &lt;tr&gt;&lt;td&gt;Copyright (c) 2004, Ernst Hairer&lt;/td&gt;&lt;/tr&gt;<a name="line.67"></a>
<FONT color="green">068</FONT>     *<a name="line.68"></a>
<FONT color="green">069</FONT>     * &lt;tr&gt;&lt;td&gt;Redistribution and use in source and binary forms, with or<a name="line.69"></a>
<FONT color="green">070</FONT>     * without modification, are permitted provided that the following<a name="line.70"></a>
<FONT color="green">071</FONT>     * conditions are met:<a name="line.71"></a>
<FONT color="green">072</FONT>     * &lt;ul&gt;<a name="line.72"></a>
<FONT color="green">073</FONT>     *  &lt;li&gt;Redistributions of source code must retain the above copyright<a name="line.73"></a>
<FONT color="green">074</FONT>     *      notice, this list of conditions and the following disclaimer.&lt;/li&gt;<a name="line.74"></a>
<FONT color="green">075</FONT>     *  &lt;li&gt;Redistributions in binary form must reproduce the above copyright<a name="line.75"></a>
<FONT color="green">076</FONT>     *      notice, this list of conditions and the following disclaimer in the<a name="line.76"></a>
<FONT color="green">077</FONT>     *      documentation and/or other materials provided with the distribution.&lt;/li&gt;<a name="line.77"></a>
<FONT color="green">078</FONT>     * &lt;/ul&gt;&lt;/td&gt;&lt;/tr&gt;<a name="line.78"></a>
<FONT color="green">079</FONT>     *<a name="line.79"></a>
<FONT color="green">080</FONT>     * &lt;tr&gt;&lt;td&gt;&lt;strong&gt;THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND<a name="line.80"></a>
<FONT color="green">081</FONT>     * CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING,<a name="line.81"></a>
<FONT color="green">082</FONT>     * BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS<a name="line.82"></a>
<FONT color="green">083</FONT>     * FOR A  PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR<a name="line.83"></a>
<FONT color="green">084</FONT>     * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,<a name="line.84"></a>
<FONT color="green">085</FONT>     * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,<a name="line.85"></a>
<FONT color="green">086</FONT>     * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR<a name="line.86"></a>
<FONT color="green">087</FONT>     * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF<a name="line.87"></a>
<FONT color="green">088</FONT>     * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING<a name="line.88"></a>
<FONT color="green">089</FONT>     * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS<a name="line.89"></a>
<FONT color="green">090</FONT>     * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.&lt;/strong&gt;&lt;/td&gt;&lt;/tr&gt;<a name="line.90"></a>
<FONT color="green">091</FONT>     * &lt;/table&gt;<a name="line.91"></a>
<FONT color="green">092</FONT>     *<a name="line.92"></a>
<FONT color="green">093</FONT>     * @version $Id: GraggBulirschStoerIntegrator.java 1416643 2012-12-03 19:37:14Z tn $<a name="line.93"></a>
<FONT color="green">094</FONT>     * @since 1.2<a name="line.94"></a>
<FONT color="green">095</FONT>     */<a name="line.95"></a>
<FONT color="green">096</FONT>    <a name="line.96"></a>
<FONT color="green">097</FONT>    public class GraggBulirschStoerIntegrator extends AdaptiveStepsizeIntegrator {<a name="line.97"></a>
<FONT color="green">098</FONT>    <a name="line.98"></a>
<FONT color="green">099</FONT>        /** Integrator method name. */<a name="line.99"></a>
<FONT color="green">100</FONT>        private static final String METHOD_NAME = "Gragg-Bulirsch-Stoer";<a name="line.100"></a>
<FONT color="green">101</FONT>    <a name="line.101"></a>
<FONT color="green">102</FONT>        /** maximal order. */<a name="line.102"></a>
<FONT color="green">103</FONT>        private int maxOrder;<a name="line.103"></a>
<FONT color="green">104</FONT>    <a name="line.104"></a>
<FONT color="green">105</FONT>        /** step size sequence. */<a name="line.105"></a>
<FONT color="green">106</FONT>        private int[] sequence;<a name="line.106"></a>
<FONT color="green">107</FONT>    <a name="line.107"></a>
<FONT color="green">108</FONT>        /** overall cost of applying step reduction up to iteration k+1, in number of calls. */<a name="line.108"></a>
<FONT color="green">109</FONT>        private int[] costPerStep;<a name="line.109"></a>
<FONT color="green">110</FONT>    <a name="line.110"></a>
<FONT color="green">111</FONT>        /** cost per unit step. */<a name="line.111"></a>
<FONT color="green">112</FONT>        private double[] costPerTimeUnit;<a name="line.112"></a>
<FONT color="green">113</FONT>    <a name="line.113"></a>
<FONT color="green">114</FONT>        /** optimal steps for each order. */<a name="line.114"></a>
<FONT color="green">115</FONT>        private double[] optimalStep;<a name="line.115"></a>
<FONT color="green">116</FONT>    <a name="line.116"></a>
<FONT color="green">117</FONT>        /** extrapolation coefficients. */<a name="line.117"></a>
<FONT color="green">118</FONT>        private double[][] coeff;<a name="line.118"></a>
<FONT color="green">119</FONT>    <a name="line.119"></a>
<FONT color="green">120</FONT>        /** stability check enabling parameter. */<a name="line.120"></a>
<FONT color="green">121</FONT>        private boolean performTest;<a name="line.121"></a>
<FONT color="green">122</FONT>    <a name="line.122"></a>
<FONT color="green">123</FONT>        /** maximal number of checks for each iteration. */<a name="line.123"></a>
<FONT color="green">124</FONT>        private int maxChecks;<a name="line.124"></a>
<FONT color="green">125</FONT>    <a name="line.125"></a>
<FONT color="green">126</FONT>        /** maximal number of iterations for which checks are performed. */<a name="line.126"></a>
<FONT color="green">127</FONT>        private int maxIter;<a name="line.127"></a>
<FONT color="green">128</FONT>    <a name="line.128"></a>
<FONT color="green">129</FONT>        /** stepsize reduction factor in case of stability check failure. */<a name="line.129"></a>
<FONT color="green">130</FONT>        private double stabilityReduction;<a name="line.130"></a>
<FONT color="green">131</FONT>    <a name="line.131"></a>
<FONT color="green">132</FONT>        /** first stepsize control factor. */<a name="line.132"></a>
<FONT color="green">133</FONT>        private double stepControl1;<a name="line.133"></a>
<FONT color="green">134</FONT>    <a name="line.134"></a>
<FONT color="green">135</FONT>        /** second stepsize control factor. */<a name="line.135"></a>
<FONT color="green">136</FONT>        private double stepControl2;<a name="line.136"></a>
<FONT color="green">137</FONT>    <a name="line.137"></a>
<FONT color="green">138</FONT>        /** third stepsize control factor. */<a name="line.138"></a>
<FONT color="green">139</FONT>        private double stepControl3;<a name="line.139"></a>
<FONT color="green">140</FONT>    <a name="line.140"></a>
<FONT color="green">141</FONT>        /** fourth stepsize control factor. */<a name="line.141"></a>
<FONT color="green">142</FONT>        private double stepControl4;<a name="line.142"></a>
<FONT color="green">143</FONT>    <a name="line.143"></a>
<FONT color="green">144</FONT>        /** first order control factor. */<a name="line.144"></a>
<FONT color="green">145</FONT>        private double orderControl1;<a name="line.145"></a>
<FONT color="green">146</FONT>    <a name="line.146"></a>
<FONT color="green">147</FONT>        /** second order control factor. */<a name="line.147"></a>
<FONT color="green">148</FONT>        private double orderControl2;<a name="line.148"></a>
<FONT color="green">149</FONT>    <a name="line.149"></a>
<FONT color="green">150</FONT>        /** use interpolation error in stepsize control. */<a name="line.150"></a>
<FONT color="green">151</FONT>        private boolean useInterpolationError;<a name="line.151"></a>
<FONT color="green">152</FONT>    <a name="line.152"></a>
<FONT color="green">153</FONT>        /** interpolation order control parameter. */<a name="line.153"></a>
<FONT color="green">154</FONT>        private int mudif;<a name="line.154"></a>
<FONT color="green">155</FONT>    <a name="line.155"></a>
<FONT color="green">156</FONT>      /** Simple constructor.<a name="line.156"></a>
<FONT color="green">157</FONT>       * Build a Gragg-Bulirsch-Stoer integrator with the given step<a name="line.157"></a>
<FONT color="green">158</FONT>       * bounds. All tuning parameters are set to their default<a name="line.158"></a>
<FONT color="green">159</FONT>       * values. The default step handler does nothing.<a name="line.159"></a>
<FONT color="green">160</FONT>       * @param minStep minimal step (sign is irrelevant, regardless of<a name="line.160"></a>
<FONT color="green">161</FONT>       * integration direction, forward or backward), the last step can<a name="line.161"></a>
<FONT color="green">162</FONT>       * be smaller than this<a name="line.162"></a>
<FONT color="green">163</FONT>       * @param maxStep maximal step (sign is irrelevant, regardless of<a name="line.163"></a>
<FONT color="green">164</FONT>       * integration direction, forward or backward), the last step can<a name="line.164"></a>
<FONT color="green">165</FONT>       * be smaller than this<a name="line.165"></a>
<FONT color="green">166</FONT>       * @param scalAbsoluteTolerance allowed absolute error<a name="line.166"></a>
<FONT color="green">167</FONT>       * @param scalRelativeTolerance allowed relative error<a name="line.167"></a>
<FONT color="green">168</FONT>       */<a name="line.168"></a>
<FONT color="green">169</FONT>      public GraggBulirschStoerIntegrator(final double minStep, final double maxStep,<a name="line.169"></a>
<FONT color="green">170</FONT>                                          final double scalAbsoluteTolerance,<a name="line.170"></a>
<FONT color="green">171</FONT>                                          final double scalRelativeTolerance) {<a name="line.171"></a>
<FONT color="green">172</FONT>        super(METHOD_NAME, minStep, maxStep,<a name="line.172"></a>
<FONT color="green">173</FONT>              scalAbsoluteTolerance, scalRelativeTolerance);<a name="line.173"></a>
<FONT color="green">174</FONT>        setStabilityCheck(true, -1, -1, -1);<a name="line.174"></a>
<FONT color="green">175</FONT>        setControlFactors(-1, -1, -1, -1);<a name="line.175"></a>
<FONT color="green">176</FONT>        setOrderControl(-1, -1, -1);<a name="line.176"></a>
<FONT color="green">177</FONT>        setInterpolationControl(true, -1);<a name="line.177"></a>
<FONT color="green">178</FONT>      }<a name="line.178"></a>
<FONT color="green">179</FONT>    <a name="line.179"></a>
<FONT color="green">180</FONT>      /** Simple constructor.<a name="line.180"></a>
<FONT color="green">181</FONT>       * Build a Gragg-Bulirsch-Stoer integrator with the given step<a name="line.181"></a>
<FONT color="green">182</FONT>       * bounds. All tuning parameters are set to their default<a name="line.182"></a>
<FONT color="green">183</FONT>       * values. The default step handler does nothing.<a name="line.183"></a>
<FONT color="green">184</FONT>       * @param minStep minimal step (must be positive even for backward<a name="line.184"></a>
<FONT color="green">185</FONT>       * integration), the last step can be smaller than this<a name="line.185"></a>
<FONT color="green">186</FONT>       * @param maxStep maximal step (must be positive even for backward<a name="line.186"></a>
<FONT color="green">187</FONT>       * integration)<a name="line.187"></a>
<FONT color="green">188</FONT>       * @param vecAbsoluteTolerance allowed absolute error<a name="line.188"></a>
<FONT color="green">189</FONT>       * @param vecRelativeTolerance allowed relative error<a name="line.189"></a>
<FONT color="green">190</FONT>       */<a name="line.190"></a>
<FONT color="green">191</FONT>      public GraggBulirschStoerIntegrator(final double minStep, final double maxStep,<a name="line.191"></a>
<FONT color="green">192</FONT>                                          final double[] vecAbsoluteTolerance,<a name="line.192"></a>
<FONT color="green">193</FONT>                                          final double[] vecRelativeTolerance) {<a name="line.193"></a>
<FONT color="green">194</FONT>        super(METHOD_NAME, minStep, maxStep,<a name="line.194"></a>
<FONT color="green">195</FONT>              vecAbsoluteTolerance, vecRelativeTolerance);<a name="line.195"></a>
<FONT color="green">196</FONT>        setStabilityCheck(true, -1, -1, -1);<a name="line.196"></a>
<FONT color="green">197</FONT>        setControlFactors(-1, -1, -1, -1);<a name="line.197"></a>
<FONT color="green">198</FONT>        setOrderControl(-1, -1, -1);<a name="line.198"></a>
<FONT color="green">199</FONT>        setInterpolationControl(true, -1);<a name="line.199"></a>
<FONT color="green">200</FONT>      }<a name="line.200"></a>
<FONT color="green">201</FONT>    <a name="line.201"></a>
<FONT color="green">202</FONT>      /** Set the stability check controls.<a name="line.202"></a>
<FONT color="green">203</FONT>       * &lt;p&gt;The stability check is performed on the first few iterations of<a name="line.203"></a>
<FONT color="green">204</FONT>       * the extrapolation scheme. If this test fails, the step is rejected<a name="line.204"></a>
<FONT color="green">205</FONT>       * and the stepsize is reduced.&lt;/p&gt;<a name="line.205"></a>
<FONT color="green">206</FONT>       * &lt;p&gt;By default, the test is performed, at most during two<a name="line.206"></a>
<FONT color="green">207</FONT>       * iterations at each step, and at most once for each of these<a name="line.207"></a>
<FONT color="green">208</FONT>       * iterations. The default stepsize reduction factor is 0.5.&lt;/p&gt;<a name="line.208"></a>
<FONT color="green">209</FONT>       * @param performStabilityCheck if true, stability check will be performed,<a name="line.209"></a>
<FONT color="green">210</FONT>         if false, the check will be skipped<a name="line.210"></a>
<FONT color="green">211</FONT>       * @param maxNumIter maximal number of iterations for which checks are<a name="line.211"></a>
<FONT color="green">212</FONT>       * performed (the number of iterations is reset to default if negative<a name="line.212"></a>
<FONT color="green">213</FONT>       * or null)<a name="line.213"></a>
<FONT color="green">214</FONT>       * @param maxNumChecks maximal number of checks for each iteration<a name="line.214"></a>
<FONT color="green">215</FONT>       * (the number of checks is reset to default if negative or null)<a name="line.215"></a>
<FONT color="green">216</FONT>       * @param stepsizeReductionFactor stepsize reduction factor in case of<a name="line.216"></a>
<FONT color="green">217</FONT>       * failure (the factor is reset to default if lower than 0.0001 or<a name="line.217"></a>
<FONT color="green">218</FONT>       * greater than 0.9999)<a name="line.218"></a>
<FONT color="green">219</FONT>       */<a name="line.219"></a>
<FONT color="green">220</FONT>      public void setStabilityCheck(final boolean performStabilityCheck,<a name="line.220"></a>
<FONT color="green">221</FONT>                                    final int maxNumIter, final int maxNumChecks,<a name="line.221"></a>
<FONT color="green">222</FONT>                                    final double stepsizeReductionFactor) {<a name="line.222"></a>
<FONT color="green">223</FONT>    <a name="line.223"></a>
<FONT color="green">224</FONT>        this.performTest = performStabilityCheck;<a name="line.224"></a>
<FONT color="green">225</FONT>        this.maxIter     = (maxNumIter   &lt;= 0) ? 2 : maxNumIter;<a name="line.225"></a>
<FONT color="green">226</FONT>        this.maxChecks   = (maxNumChecks &lt;= 0) ? 1 : maxNumChecks;<a name="line.226"></a>
<FONT color="green">227</FONT>    <a name="line.227"></a>
<FONT color="green">228</FONT>        if ((stepsizeReductionFactor &lt; 0.0001) || (stepsizeReductionFactor &gt; 0.9999)) {<a name="line.228"></a>
<FONT color="green">229</FONT>          this.stabilityReduction = 0.5;<a name="line.229"></a>
<FONT color="green">230</FONT>        } else {<a name="line.230"></a>
<FONT color="green">231</FONT>          this.stabilityReduction = stepsizeReductionFactor;<a name="line.231"></a>
<FONT color="green">232</FONT>        }<a name="line.232"></a>
<FONT color="green">233</FONT>    <a name="line.233"></a>
<FONT color="green">234</FONT>      }<a name="line.234"></a>
<FONT color="green">235</FONT>    <a name="line.235"></a>
<FONT color="green">236</FONT>      /** Set the step size control factors.<a name="line.236"></a>
<FONT color="green">237</FONT>    <a name="line.237"></a>
<FONT color="green">238</FONT>       * &lt;p&gt;The new step size hNew is computed from the old one h by:<a name="line.238"></a>
<FONT color="green">239</FONT>       * &lt;pre&gt;<a name="line.239"></a>
<FONT color="green">240</FONT>       * hNew = h * stepControl2 / (err/stepControl1)^(1/(2k+1))<a name="line.240"></a>
<FONT color="green">241</FONT>       * &lt;/pre&gt;<a name="line.241"></a>
<FONT color="green">242</FONT>       * where err is the scaled error and k the iteration number of the<a name="line.242"></a>
<FONT color="green">243</FONT>       * extrapolation scheme (counting from 0). The default values are<a name="line.243"></a>
<FONT color="green">244</FONT>       * 0.65 for stepControl1 and 0.94 for stepControl2.&lt;/p&gt;<a name="line.244"></a>
<FONT color="green">245</FONT>       * &lt;p&gt;The step size is subject to the restriction:<a name="line.245"></a>
<FONT color="green">246</FONT>       * &lt;pre&gt;<a name="line.246"></a>
<FONT color="green">247</FONT>       * stepControl3^(1/(2k+1))/stepControl4 &lt;= hNew/h &lt;= 1/stepControl3^(1/(2k+1))<a name="line.247"></a>
<FONT color="green">248</FONT>       * &lt;/pre&gt;<a name="line.248"></a>
<FONT color="green">249</FONT>       * The default values are 0.02 for stepControl3 and 4.0 for<a name="line.249"></a>
<FONT color="green">250</FONT>       * stepControl4.&lt;/p&gt;<a name="line.250"></a>
<FONT color="green">251</FONT>       * @param control1 first stepsize control factor (the factor is<a name="line.251"></a>
<FONT color="green">252</FONT>       * reset to default if lower than 0.0001 or greater than 0.9999)<a name="line.252"></a>
<FONT color="green">253</FONT>       * @param control2 second stepsize control factor (the factor<a name="line.253"></a>
<FONT color="green">254</FONT>       * is reset to default if lower than 0.0001 or greater than 0.9999)<a name="line.254"></a>
<FONT color="green">255</FONT>       * @param control3 third stepsize control factor (the factor is<a name="line.255"></a>
<FONT color="green">256</FONT>       * reset to default if lower than 0.0001 or greater than 0.9999)<a name="line.256"></a>
<FONT color="green">257</FONT>       * @param control4 fourth stepsize control factor (the factor<a name="line.257"></a>
<FONT color="green">258</FONT>       * is reset to default if lower than 1.0001 or greater than 999.9)<a name="line.258"></a>
<FONT color="green">259</FONT>       */<a name="line.259"></a>
<FONT color="green">260</FONT>      public void setControlFactors(final double control1, final double control2,<a name="line.260"></a>
<FONT color="green">261</FONT>                                    final double control3, final double control4) {<a name="line.261"></a>
<FONT color="green">262</FONT>    <a name="line.262"></a>
<FONT color="green">263</FONT>        if ((control1 &lt; 0.0001) || (control1 &gt; 0.9999)) {<a name="line.263"></a>
<FONT color="green">264</FONT>          this.stepControl1 = 0.65;<a name="line.264"></a>
<FONT color="green">265</FONT>        } else {<a name="line.265"></a>
<FONT color="green">266</FONT>          this.stepControl1 = control1;<a name="line.266"></a>
<FONT color="green">267</FONT>        }<a name="line.267"></a>
<FONT color="green">268</FONT>    <a name="line.268"></a>
<FONT color="green">269</FONT>        if ((control2 &lt; 0.0001) || (control2 &gt; 0.9999)) {<a name="line.269"></a>
<FONT color="green">270</FONT>          this.stepControl2 = 0.94;<a name="line.270"></a>
<FONT color="green">271</FONT>        } else {<a name="line.271"></a>
<FONT color="green">272</FONT>          this.stepControl2 = control2;<a name="line.272"></a>
<FONT color="green">273</FONT>        }<a name="line.273"></a>
<FONT color="green">274</FONT>    <a name="line.274"></a>
<FONT color="green">275</FONT>        if ((control3 &lt; 0.0001) || (control3 &gt; 0.9999)) {<a name="line.275"></a>
<FONT color="green">276</FONT>          this.stepControl3 = 0.02;<a name="line.276"></a>
<FONT color="green">277</FONT>        } else {<a name="line.277"></a>
<FONT color="green">278</FONT>          this.stepControl3 = control3;<a name="line.278"></a>
<FONT color="green">279</FONT>        }<a name="line.279"></a>
<FONT color="green">280</FONT>    <a name="line.280"></a>
<FONT color="green">281</FONT>        if ((control4 &lt; 1.0001) || (control4 &gt; 999.9)) {<a name="line.281"></a>
<FONT color="green">282</FONT>          this.stepControl4 = 4.0;<a name="line.282"></a>
<FONT color="green">283</FONT>        } else {<a name="line.283"></a>
<FONT color="green">284</FONT>          this.stepControl4 = control4;<a name="line.284"></a>
<FONT color="green">285</FONT>        }<a name="line.285"></a>
<FONT color="green">286</FONT>    <a name="line.286"></a>
<FONT color="green">287</FONT>      }<a name="line.287"></a>
<FONT color="green">288</FONT>    <a name="line.288"></a>
<FONT color="green">289</FONT>      /** Set the order control parameters.<a name="line.289"></a>
<FONT color="green">290</FONT>       * &lt;p&gt;The Gragg-Bulirsch-Stoer method changes both the step size and<a name="line.290"></a>
<FONT color="green">291</FONT>       * the order during integration, in order to minimize computation<a name="line.291"></a>
<FONT color="green">292</FONT>       * cost. Each extrapolation step increases the order by 2, so the<a name="line.292"></a>
<FONT color="green">293</FONT>       * maximal order that will be used is always even, it is twice the<a name="line.293"></a>
<FONT color="green">294</FONT>       * maximal number of columns in the extrapolation table.&lt;/p&gt;<a name="line.294"></a>
<FONT color="green">295</FONT>       * &lt;pre&gt;<a name="line.295"></a>
<FONT color="green">296</FONT>       * order is decreased if w(k-1) &lt;= w(k)   * orderControl1<a name="line.296"></a>
<FONT color="green">297</FONT>       * order is increased if w(k)   &lt;= w(k-1) * orderControl2<a name="line.297"></a>
<FONT color="green">298</FONT>       * &lt;/pre&gt;<a name="line.298"></a>
<FONT color="green">299</FONT>       * &lt;p&gt;where w is the table of work per unit step for each order<a name="line.299"></a>
<FONT color="green">300</FONT>       * (number of function calls divided by the step length), and k is<a name="line.300"></a>
<FONT color="green">301</FONT>       * the current order.&lt;/p&gt;<a name="line.301"></a>
<FONT color="green">302</FONT>       * &lt;p&gt;The default maximal order after construction is 18 (i.e. the<a name="line.302"></a>
<FONT color="green">303</FONT>       * maximal number of columns is 9). The default values are 0.8 for<a name="line.303"></a>
<FONT color="green">304</FONT>       * orderControl1 and 0.9 for orderControl2.&lt;/p&gt;<a name="line.304"></a>
<FONT color="green">305</FONT>       * @param maximalOrder maximal order in the extrapolation table (the<a name="line.305"></a>
<FONT color="green">306</FONT>       * maximal order is reset to default if order &lt;= 6 or odd)<a name="line.306"></a>
<FONT color="green">307</FONT>       * @param control1 first order control factor (the factor is<a name="line.307"></a>
<FONT color="green">308</FONT>       * reset to default if lower than 0.0001 or greater than 0.9999)<a name="line.308"></a>
<FONT color="green">309</FONT>       * @param control2 second order control factor (the factor<a name="line.309"></a>
<FONT color="green">310</FONT>       * is reset to default if lower than 0.0001 or greater than 0.9999)<a name="line.310"></a>
<FONT color="green">311</FONT>       */<a name="line.311"></a>
<FONT color="green">312</FONT>      public void setOrderControl(final int maximalOrder,<a name="line.312"></a>
<FONT color="green">313</FONT>                                  final double control1, final double control2) {<a name="line.313"></a>
<FONT color="green">314</FONT>    <a name="line.314"></a>
<FONT color="green">315</FONT>        if ((maximalOrder &lt;= 6) || (maximalOrder % 2 != 0)) {<a name="line.315"></a>
<FONT color="green">316</FONT>          this.maxOrder = 18;<a name="line.316"></a>
<FONT color="green">317</FONT>        }<a name="line.317"></a>
<FONT color="green">318</FONT>    <a name="line.318"></a>
<FONT color="green">319</FONT>        if ((control1 &lt; 0.0001) || (control1 &gt; 0.9999)) {<a name="line.319"></a>
<FONT color="green">320</FONT>          this.orderControl1 = 0.8;<a name="line.320"></a>
<FONT color="green">321</FONT>        } else {<a name="line.321"></a>
<FONT color="green">322</FONT>          this.orderControl1 = control1;<a name="line.322"></a>
<FONT color="green">323</FONT>        }<a name="line.323"></a>
<FONT color="green">324</FONT>    <a name="line.324"></a>
<FONT color="green">325</FONT>        if ((control2 &lt; 0.0001) || (control2 &gt; 0.9999)) {<a name="line.325"></a>
<FONT color="green">326</FONT>          this.orderControl2 = 0.9;<a name="line.326"></a>
<FONT color="green">327</FONT>        } else {<a name="line.327"></a>
<FONT color="green">328</FONT>          this.orderControl2 = control2;<a name="line.328"></a>
<FONT color="green">329</FONT>        }<a name="line.329"></a>
<FONT color="green">330</FONT>    <a name="line.330"></a>
<FONT color="green">331</FONT>        // reinitialize the arrays<a name="line.331"></a>
<FONT color="green">332</FONT>        initializeArrays();<a name="line.332"></a>
<FONT color="green">333</FONT>    <a name="line.333"></a>
<FONT color="green">334</FONT>      }<a name="line.334"></a>
<FONT color="green">335</FONT>    <a name="line.335"></a>
<FONT color="green">336</FONT>      /** {@inheritDoc} */<a name="line.336"></a>
<FONT color="green">337</FONT>      @Override<a name="line.337"></a>
<FONT color="green">338</FONT>      public void addStepHandler (final StepHandler handler) {<a name="line.338"></a>
<FONT color="green">339</FONT>    <a name="line.339"></a>
<FONT color="green">340</FONT>        super.addStepHandler(handler);<a name="line.340"></a>
<FONT color="green">341</FONT>    <a name="line.341"></a>
<FONT color="green">342</FONT>        // reinitialize the arrays<a name="line.342"></a>
<FONT color="green">343</FONT>        initializeArrays();<a name="line.343"></a>
<FONT color="green">344</FONT>    <a name="line.344"></a>
<FONT color="green">345</FONT>      }<a name="line.345"></a>
<FONT color="green">346</FONT>    <a name="line.346"></a>
<FONT color="green">347</FONT>      /** {@inheritDoc} */<a name="line.347"></a>
<FONT color="green">348</FONT>      @Override<a name="line.348"></a>
<FONT color="green">349</FONT>      public void addEventHandler(final EventHandler function,<a name="line.349"></a>
<FONT color="green">350</FONT>                                  final double maxCheckInterval,<a name="line.350"></a>
<FONT color="green">351</FONT>                                  final double convergence,<a name="line.351"></a>
<FONT color="green">352</FONT>                                  final int maxIterationCount,<a name="line.352"></a>
<FONT color="green">353</FONT>                                  final UnivariateSolver solver) {<a name="line.353"></a>
<FONT color="green">354</FONT>        super.addEventHandler(function, maxCheckInterval, convergence,<a name="line.354"></a>
<FONT color="green">355</FONT>                              maxIterationCount, solver);<a name="line.355"></a>
<FONT color="green">356</FONT>    <a name="line.356"></a>
<FONT color="green">357</FONT>        // reinitialize the arrays<a name="line.357"></a>
<FONT color="green">358</FONT>        initializeArrays();<a name="line.358"></a>
<FONT color="green">359</FONT>    <a name="line.359"></a>
<FONT color="green">360</FONT>      }<a name="line.360"></a>
<FONT color="green">361</FONT>    <a name="line.361"></a>
<FONT color="green">362</FONT>      /** Initialize the integrator internal arrays. */<a name="line.362"></a>
<FONT color="green">363</FONT>      private void initializeArrays() {<a name="line.363"></a>
<FONT color="green">364</FONT>    <a name="line.364"></a>
<FONT color="green">365</FONT>        final int size = maxOrder / 2;<a name="line.365"></a>
<FONT color="green">366</FONT>    <a name="line.366"></a>
<FONT color="green">367</FONT>        if ((sequence == null) || (sequence.length != size)) {<a name="line.367"></a>
<FONT color="green">368</FONT>          // all arrays should be reallocated with the right size<a name="line.368"></a>
<FONT color="green">369</FONT>          sequence        = new int[size];<a name="line.369"></a>
<FONT color="green">370</FONT>          costPerStep     = new int[size];<a name="line.370"></a>
<FONT color="green">371</FONT>          coeff           = new double[size][];<a name="line.371"></a>
<FONT color="green">372</FONT>          costPerTimeUnit = new double[size];<a name="line.372"></a>
<FONT color="green">373</FONT>          optimalStep     = new double[size];<a name="line.373"></a>
<FONT color="green">374</FONT>        }<a name="line.374"></a>
<FONT color="green">375</FONT>    <a name="line.375"></a>
<FONT color="green">376</FONT>        // step size sequence: 2, 6, 10, 14, ...<a name="line.376"></a>
<FONT color="green">377</FONT>        for (int k = 0; k &lt; size; ++k) {<a name="line.377"></a>
<FONT color="green">378</FONT>            sequence[k] = 4 * k + 2;<a name="line.378"></a>
<FONT color="green">379</FONT>        }<a name="line.379"></a>
<FONT color="green">380</FONT>    <a name="line.380"></a>
<FONT color="green">381</FONT>        // initialize the order selection cost array<a name="line.381"></a>
<FONT color="green">382</FONT>        // (number of function calls for each column of the extrapolation table)<a name="line.382"></a>
<FONT color="green">383</FONT>        costPerStep[0] = sequence[0] + 1;<a name="line.383"></a>
<FONT color="green">384</FONT>        for (int k = 1; k &lt; size; ++k) {<a name="line.384"></a>
<FONT color="green">385</FONT>          costPerStep[k] = costPerStep[k-1] + sequence[k];<a name="line.385"></a>
<FONT color="green">386</FONT>        }<a name="line.386"></a>
<FONT color="green">387</FONT>    <a name="line.387"></a>
<FONT color="green">388</FONT>        // initialize the extrapolation tables<a name="line.388"></a>
<FONT color="green">389</FONT>        for (int k = 0; k &lt; size; ++k) {<a name="line.389"></a>
<FONT color="green">390</FONT>          coeff[k] = (k &gt; 0) ? new double[k] : null;<a name="line.390"></a>
<FONT color="green">391</FONT>          for (int l = 0; l &lt; k; ++l) {<a name="line.391"></a>
<FONT color="green">392</FONT>            final double ratio = ((double) sequence[k]) / sequence[k-l-1];<a name="line.392"></a>
<FONT color="green">393</FONT>            coeff[k][l] = 1.0 / (ratio * ratio - 1.0);<a name="line.393"></a>
<FONT color="green">394</FONT>          }<a name="line.394"></a>
<FONT color="green">395</FONT>        }<a name="line.395"></a>
<FONT color="green">396</FONT>    <a name="line.396"></a>
<FONT color="green">397</FONT>      }<a name="line.397"></a>
<FONT color="green">398</FONT>    <a name="line.398"></a>
<FONT color="green">399</FONT>      /** Set the interpolation order control parameter.<a name="line.399"></a>
<FONT color="green">400</FONT>       * The interpolation order for dense output is 2k - mudif + 1. The<a name="line.400"></a>
<FONT color="green">401</FONT>       * default value for mudif is 4 and the interpolation error is used<a name="line.401"></a>
<FONT color="green">402</FONT>       * in stepsize control by default.<a name="line.402"></a>
<FONT color="green">403</FONT>    <a name="line.403"></a>
<FONT color="green">404</FONT>       * @param useInterpolationErrorForControl if true, interpolation error is used<a name="line.404"></a>
<FONT color="green">405</FONT>       * for stepsize control<a name="line.405"></a>
<FONT color="green">406</FONT>       * @param mudifControlParameter interpolation order control parameter (the parameter<a name="line.406"></a>
<FONT color="green">407</FONT>       * is reset to default if &lt;= 0 or &gt;= 7)<a name="line.407"></a>
<FONT color="green">408</FONT>       */<a name="line.408"></a>
<FONT color="green">409</FONT>      public void setInterpolationControl(final boolean useInterpolationErrorForControl,<a name="line.409"></a>
<FONT color="green">410</FONT>                                          final int mudifControlParameter) {<a name="line.410"></a>
<FONT color="green">411</FONT>    <a name="line.411"></a>
<FONT color="green">412</FONT>        this.useInterpolationError = useInterpolationErrorForControl;<a name="line.412"></a>
<FONT color="green">413</FONT>    <a name="line.413"></a>
<FONT color="green">414</FONT>        if ((mudifControlParameter &lt;= 0) || (mudifControlParameter &gt;= 7)) {<a name="line.414"></a>
<FONT color="green">415</FONT>          this.mudif = 4;<a name="line.415"></a>
<FONT color="green">416</FONT>        } else {<a name="line.416"></a>
<FONT color="green">417</FONT>          this.mudif = mudifControlParameter;<a name="line.417"></a>
<FONT color="green">418</FONT>        }<a name="line.418"></a>
<FONT color="green">419</FONT>    <a name="line.419"></a>
<FONT color="green">420</FONT>      }<a name="line.420"></a>
<FONT color="green">421</FONT>    <a name="line.421"></a>
<FONT color="green">422</FONT>      /** Update scaling array.<a name="line.422"></a>
<FONT color="green">423</FONT>       * @param y1 first state vector to use for scaling<a name="line.423"></a>
<FONT color="green">424</FONT>       * @param y2 second state vector to use for scaling<a name="line.424"></a>
<FONT color="green">425</FONT>       * @param scale scaling array to update (can be shorter than state)<a name="line.425"></a>
<FONT color="green">426</FONT>       */<a name="line.426"></a>
<FONT color="green">427</FONT>      private void rescale(final double[] y1, final double[] y2, final double[] scale) {<a name="line.427"></a>
<FONT color="green">428</FONT>        if (vecAbsoluteTolerance == null) {<a name="line.428"></a>
<FONT color="green">429</FONT>          for (int i = 0; i &lt; scale.length; ++i) {<a name="line.429"></a>
<FONT color="green">430</FONT>            final double yi = FastMath.max(FastMath.abs(y1[i]), FastMath.abs(y2[i]));<a name="line.430"></a>
<FONT color="green">431</FONT>            scale[i] = scalAbsoluteTolerance + scalRelativeTolerance * yi;<a name="line.431"></a>
<FONT color="green">432</FONT>          }<a name="line.432"></a>
<FONT color="green">433</FONT>        } else {<a name="line.433"></a>
<FONT color="green">434</FONT>          for (int i = 0; i &lt; scale.length; ++i) {<a name="line.434"></a>
<FONT color="green">435</FONT>            final double yi = FastMath.max(FastMath.abs(y1[i]), FastMath.abs(y2[i]));<a name="line.435"></a>
<FONT color="green">436</FONT>            scale[i] = vecAbsoluteTolerance[i] + vecRelativeTolerance[i] * yi;<a name="line.436"></a>
<FONT color="green">437</FONT>          }<a name="line.437"></a>
<FONT color="green">438</FONT>        }<a name="line.438"></a>
<FONT color="green">439</FONT>      }<a name="line.439"></a>
<FONT color="green">440</FONT>    <a name="line.440"></a>
<FONT color="green">441</FONT>      /** Perform integration over one step using substeps of a modified<a name="line.441"></a>
<FONT color="green">442</FONT>       * midpoint method.<a name="line.442"></a>
<FONT color="green">443</FONT>       * @param t0 initial time<a name="line.443"></a>
<FONT color="green">444</FONT>       * @param y0 initial value of the state vector at t0<a name="line.444"></a>
<FONT color="green">445</FONT>       * @param step global step<a name="line.445"></a>
<FONT color="green">446</FONT>       * @param k iteration number (from 0 to sequence.length - 1)<a name="line.446"></a>
<FONT color="green">447</FONT>       * @param scale scaling array (can be shorter than state)<a name="line.447"></a>
<FONT color="green">448</FONT>       * @param f placeholder where to put the state vector derivatives at each substep<a name="line.448"></a>
<FONT color="green">449</FONT>       *          (element 0 already contains initial derivative)<a name="line.449"></a>
<FONT color="green">450</FONT>       * @param yMiddle placeholder where to put the state vector at the middle of the step<a name="line.450"></a>
<FONT color="green">451</FONT>       * @param yEnd placeholder where to put the state vector at the end<a name="line.451"></a>
<FONT color="green">452</FONT>       * @param yTmp placeholder for one state vector<a name="line.452"></a>
<FONT color="green">453</FONT>       * @return true if computation was done properly,<a name="line.453"></a>
<FONT color="green">454</FONT>       *         false if stability check failed before end of computation<a name="line.454"></a>
<FONT color="green">455</FONT>       * @exception MaxCountExceededException if the number of functions evaluations is exceeded<a name="line.455"></a>
<FONT color="green">456</FONT>       * @exception DimensionMismatchException if arrays dimensions do not match equations settings<a name="line.456"></a>
<FONT color="green">457</FONT>       */<a name="line.457"></a>
<FONT color="green">458</FONT>      private boolean tryStep(final double t0, final double[] y0, final double step, final int k,<a name="line.458"></a>
<FONT color="green">459</FONT>                              final double[] scale, final double[][] f,<a name="line.459"></a>
<FONT color="green">460</FONT>                              final double[] yMiddle, final double[] yEnd,<a name="line.460"></a>
<FONT color="green">461</FONT>                              final double[] yTmp)<a name="line.461"></a>
<FONT color="green">462</FONT>          throws MaxCountExceededException, DimensionMismatchException {<a name="line.462"></a>
<FONT color="green">463</FONT>    <a name="line.463"></a>
<FONT color="green">464</FONT>        final int    n        = sequence[k];<a name="line.464"></a>
<FONT color="green">465</FONT>        final double subStep  = step / n;<a name="line.465"></a>
<FONT color="green">466</FONT>        final double subStep2 = 2 * subStep;<a name="line.466"></a>
<FONT color="green">467</FONT>    <a name="line.467"></a>
<FONT color="green">468</FONT>        // first substep<a name="line.468"></a>
<FONT color="green">469</FONT>        double t = t0 + subStep;<a name="line.469"></a>
<FONT color="green">470</FONT>        for (int i = 0; i &lt; y0.length; ++i) {<a name="line.470"></a>
<FONT color="green">471</FONT>          yTmp[i] = y0[i];<a name="line.471"></a>
<FONT color="green">472</FONT>          yEnd[i] = y0[i] + subStep * f[0][i];<a name="line.472"></a>
<FONT color="green">473</FONT>        }<a name="line.473"></a>
<FONT color="green">474</FONT>        computeDerivatives(t, yEnd, f[1]);<a name="line.474"></a>
<FONT color="green">475</FONT>    <a name="line.475"></a>
<FONT color="green">476</FONT>        // other substeps<a name="line.476"></a>
<FONT color="green">477</FONT>        for (int j = 1; j &lt; n; ++j) {<a name="line.477"></a>
<FONT color="green">478</FONT>    <a name="line.478"></a>
<FONT color="green">479</FONT>          if (2 * j == n) {<a name="line.479"></a>
<FONT color="green">480</FONT>            // save the point at the middle of the step<a name="line.480"></a>
<FONT color="green">481</FONT>            System.arraycopy(yEnd, 0, yMiddle, 0, y0.length);<a name="line.481"></a>
<FONT color="green">482</FONT>          }<a name="line.482"></a>
<FONT color="green">483</FONT>    <a name="line.483"></a>
<FONT color="green">484</FONT>          t += subStep;<a name="line.484"></a>
<FONT color="green">485</FONT>          for (int i = 0; i &lt; y0.length; ++i) {<a name="line.485"></a>
<FONT color="green">486</FONT>            final double middle = yEnd[i];<a name="line.486"></a>
<FONT color="green">487</FONT>            yEnd[i]       = yTmp[i] + subStep2 * f[j][i];<a name="line.487"></a>
<FONT color="green">488</FONT>            yTmp[i]       = middle;<a name="line.488"></a>
<FONT color="green">489</FONT>          }<a name="line.489"></a>
<FONT color="green">490</FONT>    <a name="line.490"></a>
<FONT color="green">491</FONT>          computeDerivatives(t, yEnd, f[j+1]);<a name="line.491"></a>
<FONT color="green">492</FONT>    <a name="line.492"></a>
<FONT color="green">493</FONT>          // stability check<a name="line.493"></a>
<FONT color="green">494</FONT>          if (performTest &amp;&amp; (j &lt;= maxChecks) &amp;&amp; (k &lt; maxIter)) {<a name="line.494"></a>
<FONT color="green">495</FONT>            double initialNorm = 0.0;<a name="line.495"></a>
<FONT color="green">496</FONT>            for (int l = 0; l &lt; scale.length; ++l) {<a name="line.496"></a>
<FONT color="green">497</FONT>              final double ratio = f[0][l] / scale[l];<a name="line.497"></a>
<FONT color="green">498</FONT>              initialNorm += ratio * ratio;<a name="line.498"></a>
<FONT color="green">499</FONT>            }<a name="line.499"></a>
<FONT color="green">500</FONT>            double deltaNorm = 0.0;<a name="line.500"></a>
<FONT color="green">501</FONT>            for (int l = 0; l &lt; scale.length; ++l) {<a name="line.501"></a>
<FONT color="green">502</FONT>              final double ratio = (f[j+1][l] - f[0][l]) / scale[l];<a name="line.502"></a>
<FONT color="green">503</FONT>              deltaNorm += ratio * ratio;<a name="line.503"></a>
<FONT color="green">504</FONT>            }<a name="line.504"></a>
<FONT color="green">505</FONT>            if (deltaNorm &gt; 4 * FastMath.max(1.0e-15, initialNorm)) {<a name="line.505"></a>
<FONT color="green">506</FONT>              return false;<a name="line.506"></a>
<FONT color="green">507</FONT>            }<a name="line.507"></a>
<FONT color="green">508</FONT>          }<a name="line.508"></a>
<FONT color="green">509</FONT>    <a name="line.509"></a>
<FONT color="green">510</FONT>        }<a name="line.510"></a>
<FONT color="green">511</FONT>    <a name="line.511"></a>
<FONT color="green">512</FONT>        // correction of the last substep (at t0 + step)<a name="line.512"></a>
<FONT color="green">513</FONT>        for (int i = 0; i &lt; y0.length; ++i) {<a name="line.513"></a>
<FONT color="green">514</FONT>          yEnd[i] = 0.5 * (yTmp[i] + yEnd[i] + subStep * f[n][i]);<a name="line.514"></a>
<FONT color="green">515</FONT>        }<a name="line.515"></a>
<FONT color="green">516</FONT>    <a name="line.516"></a>
<FONT color="green">517</FONT>        return true;<a name="line.517"></a>
<FONT color="green">518</FONT>    <a name="line.518"></a>
<FONT color="green">519</FONT>      }<a name="line.519"></a>
<FONT color="green">520</FONT>    <a name="line.520"></a>
<FONT color="green">521</FONT>      /** Extrapolate a vector.<a name="line.521"></a>
<FONT color="green">522</FONT>       * @param offset offset to use in the coefficients table<a name="line.522"></a>
<FONT color="green">523</FONT>       * @param k index of the last updated point<a name="line.523"></a>
<FONT color="green">524</FONT>       * @param diag working diagonal of the Aitken-Neville's<a name="line.524"></a>
<FONT color="green">525</FONT>       * triangle, without the last element<a name="line.525"></a>
<FONT color="green">526</FONT>       * @param last last element<a name="line.526"></a>
<FONT color="green">527</FONT>       */<a name="line.527"></a>
<FONT color="green">528</FONT>      private void extrapolate(final int offset, final int k,<a name="line.528"></a>
<FONT color="green">529</FONT>                               final double[][] diag, final double[] last) {<a name="line.529"></a>
<FONT color="green">530</FONT>    <a name="line.530"></a>
<FONT color="green">531</FONT>        // update the diagonal<a name="line.531"></a>
<FONT color="green">532</FONT>        for (int j = 1; j &lt; k; ++j) {<a name="line.532"></a>
<FONT color="green">533</FONT>          for (int i = 0; i &lt; last.length; ++i) {<a name="line.533"></a>
<FONT color="green">534</FONT>            // Aitken-Neville's recursive formula<a name="line.534"></a>
<FONT color="green">535</FONT>            diag[k-j-1][i] = diag[k-j][i] +<a name="line.535"></a>
<FONT color="green">536</FONT>                             coeff[k+offset][j-1] * (diag[k-j][i] - diag[k-j-1][i]);<a name="line.536"></a>
<FONT color="green">537</FONT>          }<a name="line.537"></a>
<FONT color="green">538</FONT>        }<a name="line.538"></a>
<FONT color="green">539</FONT>    <a name="line.539"></a>
<FONT color="green">540</FONT>        // update the last element<a name="line.540"></a>
<FONT color="green">541</FONT>        for (int i = 0; i &lt; last.length; ++i) {<a name="line.541"></a>
<FONT color="green">542</FONT>          // Aitken-Neville's recursive formula<a name="line.542"></a>
<FONT color="green">543</FONT>          last[i] = diag[0][i] + coeff[k+offset][k-1] * (diag[0][i] - last[i]);<a name="line.543"></a>
<FONT color="green">544</FONT>        }<a name="line.544"></a>
<FONT color="green">545</FONT>      }<a name="line.545"></a>
<FONT color="green">546</FONT>    <a name="line.546"></a>
<FONT color="green">547</FONT>      /** {@inheritDoc} */<a name="line.547"></a>
<FONT color="green">548</FONT>      @Override<a name="line.548"></a>
<FONT color="green">549</FONT>      public void integrate(final ExpandableStatefulODE equations, final double t)<a name="line.549"></a>
<FONT color="green">550</FONT>          throws NumberIsTooSmallException, DimensionMismatchException,<a name="line.550"></a>
<FONT color="green">551</FONT>                 MaxCountExceededException, NoBracketingException {<a name="line.551"></a>
<FONT color="green">552</FONT>    <a name="line.552"></a>
<FONT color="green">553</FONT>        sanityChecks(equations, t);<a name="line.553"></a>
<FONT color="green">554</FONT>        setEquations(equations);<a name="line.554"></a>
<FONT color="green">555</FONT>        final boolean forward = t &gt; equations.getTime();<a name="line.555"></a>
<FONT color="green">556</FONT>    <a name="line.556"></a>
<FONT color="green">557</FONT>        // create some internal working arrays<a name="line.557"></a>
<FONT color="green">558</FONT>        final double[] y0      = equations.getCompleteState();<a name="line.558"></a>
<FONT color="green">559</FONT>        final double[] y       = y0.clone();<a name="line.559"></a>
<FONT color="green">560</FONT>        final double[] yDot0   = new double[y.length];<a name="line.560"></a>
<FONT color="green">561</FONT>        final double[] y1      = new double[y.length];<a name="line.561"></a>
<FONT color="green">562</FONT>        final double[] yTmp    = new double[y.length];<a name="line.562"></a>
<FONT color="green">563</FONT>        final double[] yTmpDot = new double[y.length];<a name="line.563"></a>
<FONT color="green">564</FONT>    <a name="line.564"></a>
<FONT color="green">565</FONT>        final double[][] diagonal = new double[sequence.length-1][];<a name="line.565"></a>
<FONT color="green">566</FONT>        final double[][] y1Diag = new double[sequence.length-1][];<a name="line.566"></a>
<FONT color="green">567</FONT>        for (int k = 0; k &lt; sequence.length-1; ++k) {<a name="line.567"></a>
<FONT color="green">568</FONT>          diagonal[k] = new double[y.length];<a name="line.568"></a>
<FONT color="green">569</FONT>          y1Diag[k] = new double[y.length];<a name="line.569"></a>
<FONT color="green">570</FONT>        }<a name="line.570"></a>
<FONT color="green">571</FONT>    <a name="line.571"></a>
<FONT color="green">572</FONT>        final double[][][] fk  = new double[sequence.length][][];<a name="line.572"></a>
<FONT color="green">573</FONT>        for (int k = 0; k &lt; sequence.length; ++k) {<a name="line.573"></a>
<FONT color="green">574</FONT>    <a name="line.574"></a>
<FONT color="green">575</FONT>          fk[k]    = new double[sequence[k] + 1][];<a name="line.575"></a>
<FONT color="green">576</FONT>    <a name="line.576"></a>
<FONT color="green">577</FONT>          // all substeps start at the same point, so share the first array<a name="line.577"></a>
<FONT color="green">578</FONT>          fk[k][0] = yDot0;<a name="line.578"></a>
<FONT color="green">579</FONT>    <a name="line.579"></a>
<FONT color="green">580</FONT>          for (int l = 0; l &lt; sequence[k]; ++l) {<a name="line.580"></a>
<FONT color="green">581</FONT>            fk[k][l+1] = new double[y0.length];<a name="line.581"></a>
<FONT color="green">582</FONT>          }<a name="line.582"></a>
<FONT color="green">583</FONT>    <a name="line.583"></a>
<FONT color="green">584</FONT>        }<a name="line.584"></a>
<FONT color="green">585</FONT>    <a name="line.585"></a>
<FONT color="green">586</FONT>        if (y != y0) {<a name="line.586"></a>
<FONT color="green">587</FONT>          System.arraycopy(y0, 0, y, 0, y0.length);<a name="line.587"></a>
<FONT color="green">588</FONT>        }<a name="line.588"></a>
<FONT color="green">589</FONT>    <a name="line.589"></a>
<FONT color="green">590</FONT>        final double[] yDot1 = new double[y0.length];<a name="line.590"></a>
<FONT color="green">591</FONT>        final double[][] yMidDots = new double[1 + 2 * sequence.length][y0.length];<a name="line.591"></a>
<FONT color="green">592</FONT>    <a name="line.592"></a>
<FONT color="green">593</FONT>        // initial scaling<a name="line.593"></a>
<FONT color="green">594</FONT>        final double[] scale = new double[mainSetDimension];<a name="line.594"></a>
<FONT color="green">595</FONT>        rescale(y, y, scale);<a name="line.595"></a>
<FONT color="green">596</FONT>    <a name="line.596"></a>
<FONT color="green">597</FONT>        // initial order selection<a name="line.597"></a>
<FONT color="green">598</FONT>        final double tol =<a name="line.598"></a>
<FONT color="green">599</FONT>            (vecRelativeTolerance == null) ? scalRelativeTolerance : vecRelativeTolerance[0];<a name="line.599"></a>
<FONT color="green">600</FONT>        final double log10R = FastMath.log10(FastMath.max(1.0e-10, tol));<a name="line.600"></a>
<FONT color="green">601</FONT>        int targetIter = FastMath.max(1,<a name="line.601"></a>
<FONT color="green">602</FONT>                                  FastMath.min(sequence.length - 2,<a name="line.602"></a>
<FONT color="green">603</FONT>                                           (int) FastMath.floor(0.5 - 0.6 * log10R)));<a name="line.603"></a>
<FONT color="green">604</FONT>    <a name="line.604"></a>
<FONT color="green">605</FONT>        // set up an interpolator sharing the integrator arrays<a name="line.605"></a>
<FONT color="green">606</FONT>        final AbstractStepInterpolator interpolator =<a name="line.606"></a>
<FONT color="green">607</FONT>                new GraggBulirschStoerStepInterpolator(y, yDot0,<a name="line.607"></a>
<FONT color="green">608</FONT>                                                       y1, yDot1,<a name="line.608"></a>
<FONT color="green">609</FONT>                                                       yMidDots, forward,<a name="line.609"></a>
<FONT color="green">610</FONT>                                                       equations.getPrimaryMapper(),<a name="line.610"></a>
<FONT color="green">611</FONT>                                                       equations.getSecondaryMappers());<a name="line.611"></a>
<FONT color="green">612</FONT>        interpolator.storeTime(equations.getTime());<a name="line.612"></a>
<FONT color="green">613</FONT>    <a name="line.613"></a>
<FONT color="green">614</FONT>        stepStart = equations.getTime();<a name="line.614"></a>
<FONT color="green">615</FONT>        double  hNew             = 0;<a name="line.615"></a>
<FONT color="green">616</FONT>        double  maxError         = Double.MAX_VALUE;<a name="line.616"></a>
<FONT color="green">617</FONT>        boolean previousRejected = false;<a name="line.617"></a>
<FONT color="green">618</FONT>        boolean firstTime        = true;<a name="line.618"></a>
<FONT color="green">619</FONT>        boolean newStep          = true;<a name="line.619"></a>
<FONT color="green">620</FONT>        boolean firstStepAlreadyComputed = false;<a name="line.620"></a>
<FONT color="green">621</FONT>        initIntegration(equations.getTime(), y0, t);<a name="line.621"></a>
<FONT color="green">622</FONT>        costPerTimeUnit[0] = 0;<a name="line.622"></a>
<FONT color="green">623</FONT>        isLastStep = false;<a name="line.623"></a>
<FONT color="green">624</FONT>        do {<a name="line.624"></a>
<FONT color="green">625</FONT>    <a name="line.625"></a>
<FONT color="green">626</FONT>          double error;<a name="line.626"></a>
<FONT color="green">627</FONT>          boolean reject = false;<a name="line.627"></a>
<FONT color="green">628</FONT>    <a name="line.628"></a>
<FONT color="green">629</FONT>          if (newStep) {<a name="line.629"></a>
<FONT color="green">630</FONT>    <a name="line.630"></a>
<FONT color="green">631</FONT>            interpolator.shift();<a name="line.631"></a>
<FONT color="green">632</FONT>    <a name="line.632"></a>
<FONT color="green">633</FONT>            // first evaluation, at the beginning of the step<a name="line.633"></a>
<FONT color="green">634</FONT>            if (! firstStepAlreadyComputed) {<a name="line.634"></a>
<FONT color="green">635</FONT>              computeDerivatives(stepStart, y, yDot0);<a name="line.635"></a>
<FONT color="green">636</FONT>            }<a name="line.636"></a>
<FONT color="green">637</FONT>    <a name="line.637"></a>
<FONT color="green">638</FONT>            if (firstTime) {<a name="line.638"></a>
<FONT color="green">639</FONT>              hNew = initializeStep(forward, 2 * targetIter + 1, scale,<a name="line.639"></a>
<FONT color="green">640</FONT>                                    stepStart, y, yDot0, yTmp, yTmpDot);<a name="line.640"></a>
<FONT color="green">641</FONT>            }<a name="line.641"></a>
<FONT color="green">642</FONT>    <a name="line.642"></a>
<FONT color="green">643</FONT>            newStep = false;<a name="line.643"></a>
<FONT color="green">644</FONT>    <a name="line.644"></a>
<FONT color="green">645</FONT>          }<a name="line.645"></a>
<FONT color="green">646</FONT>    <a name="line.646"></a>
<FONT color="green">647</FONT>          stepSize = hNew;<a name="line.647"></a>
<FONT color="green">648</FONT>    <a name="line.648"></a>
<FONT color="green">649</FONT>          // step adjustment near bounds<a name="line.649"></a>
<FONT color="green">650</FONT>          if ((forward &amp;&amp; (stepStart + stepSize &gt; t)) ||<a name="line.650"></a>
<FONT color="green">651</FONT>              ((! forward) &amp;&amp; (stepStart + stepSize &lt; t))) {<a name="line.651"></a>
<FONT color="green">652</FONT>            stepSize = t - stepStart;<a name="line.652"></a>
<FONT color="green">653</FONT>          }<a name="line.653"></a>
<FONT color="green">654</FONT>          final double nextT = stepStart + stepSize;<a name="line.654"></a>
<FONT color="green">655</FONT>          isLastStep = forward ? (nextT &gt;= t) : (nextT &lt;= t);<a name="line.655"></a>
<FONT color="green">656</FONT>    <a name="line.656"></a>
<FONT color="green">657</FONT>          // iterate over several substep sizes<a name="line.657"></a>
<FONT color="green">658</FONT>          int k = -1;<a name="line.658"></a>
<FONT color="green">659</FONT>          for (boolean loop = true; loop; ) {<a name="line.659"></a>
<FONT color="green">660</FONT>    <a name="line.660"></a>
<FONT color="green">661</FONT>            ++k;<a name="line.661"></a>
<FONT color="green">662</FONT>    <a name="line.662"></a>
<FONT color="green">663</FONT>            // modified midpoint integration with the current substep<a name="line.663"></a>
<FONT color="green">664</FONT>            if ( ! tryStep(stepStart, y, stepSize, k, scale, fk[k],<a name="line.664"></a>
<FONT color="green">665</FONT>                           (k == 0) ? yMidDots[0] : diagonal[k-1],<a name="line.665"></a>
<FONT color="green">666</FONT>                           (k == 0) ? y1 : y1Diag[k-1],<a name="line.666"></a>
<FONT color="green">667</FONT>                           yTmp)) {<a name="line.667"></a>
<FONT color="green">668</FONT>    <a name="line.668"></a>
<FONT color="green">669</FONT>              // the stability check failed, we reduce the global step<a name="line.669"></a>
<FONT color="green">670</FONT>              hNew   = FastMath.abs(filterStep(stepSize * stabilityReduction, forward, false));<a name="line.670"></a>
<FONT color="green">671</FONT>              reject = true;<a name="line.671"></a>
<FONT color="green">672</FONT>              loop   = false;<a name="line.672"></a>
<FONT color="green">673</FONT>    <a name="line.673"></a>
<FONT color="green">674</FONT>            } else {<a name="line.674"></a>
<FONT color="green">675</FONT>    <a name="line.675"></a>
<FONT color="green">676</FONT>              // the substep was computed successfully<a name="line.676"></a>
<FONT color="green">677</FONT>              if (k &gt; 0) {<a name="line.677"></a>
<FONT color="green">678</FONT>    <a name="line.678"></a>
<FONT color="green">679</FONT>                // extrapolate the state at the end of the step<a name="line.679"></a>
<FONT color="green">680</FONT>                // using last iteration data<a name="line.680"></a>
<FONT color="green">681</FONT>                extrapolate(0, k, y1Diag, y1);<a name="line.681"></a>
<FONT color="green">682</FONT>                rescale(y, y1, scale);<a name="line.682"></a>
<FONT color="green">683</FONT>    <a name="line.683"></a>
<FONT color="green">684</FONT>                // estimate the error at the end of the step.<a name="line.684"></a>
<FONT color="green">685</FONT>                error = 0;<a name="line.685"></a>
<FONT color="green">686</FONT>                for (int j = 0; j &lt; mainSetDimension; ++j) {<a name="line.686"></a>
<FONT color="green">687</FONT>                  final double e = FastMath.abs(y1[j] - y1Diag[0][j]) / scale[j];<a name="line.687"></a>
<FONT color="green">688</FONT>                  error += e * e;<a name="line.688"></a>
<FONT color="green">689</FONT>                }<a name="line.689"></a>
<FONT color="green">690</FONT>                error = FastMath.sqrt(error / mainSetDimension);<a name="line.690"></a>
<FONT color="green">691</FONT>    <a name="line.691"></a>
<FONT color="green">692</FONT>                if ((error &gt; 1.0e15) || ((k &gt; 1) &amp;&amp; (error &gt; maxError))) {<a name="line.692"></a>
<FONT color="green">693</FONT>                  // error is too big, we reduce the global step<a name="line.693"></a>
<FONT color="green">694</FONT>                  hNew   = FastMath.abs(filterStep(stepSize * stabilityReduction, forward, false));<a name="line.694"></a>
<FONT color="green">695</FONT>                  reject = true;<a name="line.695"></a>
<FONT color="green">696</FONT>                  loop   = false;<a name="line.696"></a>
<FONT color="green">697</FONT>                } else {<a name="line.697"></a>
<FONT color="green">698</FONT>    <a name="line.698"></a>
<FONT color="green">699</FONT>                  maxError = FastMath.max(4 * error, 1.0);<a name="line.699"></a>
<FONT color="green">700</FONT>    <a name="line.700"></a>
<FONT color="green">701</FONT>                  // compute optimal stepsize for this order<a name="line.701"></a>
<FONT color="green">702</FONT>                  final double exp = 1.0 / (2 * k + 1);<a name="line.702"></a>
<FONT color="green">703</FONT>                  double fac = stepControl2 / FastMath.pow(error / stepControl1, exp);<a name="line.703"></a>
<FONT color="green">704</FONT>                  final double pow = FastMath.pow(stepControl3, exp);<a name="line.704"></a>
<FONT color="green">705</FONT>                  fac = FastMath.max(pow / stepControl4, FastMath.min(1 / pow, fac));<a name="line.705"></a>
<FONT color="green">706</FONT>                  optimalStep[k]     = FastMath.abs(filterStep(stepSize * fac, forward, true));<a name="line.706"></a>
<FONT color="green">707</FONT>                  costPerTimeUnit[k] = costPerStep[k] / optimalStep[k];<a name="line.707"></a>
<FONT color="green">708</FONT>    <a name="line.708"></a>
<FONT color="green">709</FONT>                  // check convergence<a name="line.709"></a>
<FONT color="green">710</FONT>                  switch (k - targetIter) {<a name="line.710"></a>
<FONT color="green">711</FONT>    <a name="line.711"></a>
<FONT color="green">712</FONT>                  case -1 :<a name="line.712"></a>
<FONT color="green">713</FONT>                    if ((targetIter &gt; 1) &amp;&amp; ! previousRejected) {<a name="line.713"></a>
<FONT color="green">714</FONT>    <a name="line.714"></a>
<FONT color="green">715</FONT>                      // check if we can stop iterations now<a name="line.715"></a>
<FONT color="green">716</FONT>                      if (error &lt;= 1.0) {<a name="line.716"></a>
<FONT color="green">717</FONT>                        // convergence have been reached just before targetIter<a name="line.717"></a>
<FONT color="green">718</FONT>                        loop = false;<a name="line.718"></a>
<FONT color="green">719</FONT>                      } else {<a name="line.719"></a>
<FONT color="green">720</FONT>                        // estimate if there is a chance convergence will<a name="line.720"></a>
<FONT color="green">721</FONT>                        // be reached on next iteration, using the<a name="line.721"></a>
<FONT color="green">722</FONT>                        // asymptotic evolution of error<a name="line.722"></a>
<FONT color="green">723</FONT>                        final double ratio = ((double) sequence [targetIter] * sequence[targetIter + 1]) /<a name="line.723"></a>
<FONT color="green">724</FONT>                                             (sequence[0] * sequence[0]);<a name="line.724"></a>
<FONT color="green">725</FONT>                        if (error &gt; ratio * ratio) {<a name="line.725"></a>
<FONT color="green">726</FONT>                          // we don't expect to converge on next iteration<a name="line.726"></a>
<FONT color="green">727</FONT>                          // we reject the step immediately and reduce order<a name="line.727"></a>
<FONT color="green">728</FONT>                          reject = true;<a name="line.728"></a>
<FONT color="green">729</FONT>                          loop   = false;<a name="line.729"></a>
<FONT color="green">730</FONT>                          targetIter = k;<a name="line.730"></a>
<FONT color="green">731</FONT>                          if ((targetIter &gt; 1) &amp;&amp;<a name="line.731"></a>
<FONT color="green">732</FONT>                              (costPerTimeUnit[targetIter-1] &lt;<a name="line.732"></a>
<FONT color="green">733</FONT>                               orderControl1 * costPerTimeUnit[targetIter])) {<a name="line.733"></a>
<FONT color="green">734</FONT>                            --targetIter;<a name="line.734"></a>
<FONT color="green">735</FONT>                          }<a name="line.735"></a>
<FONT color="green">736</FONT>                          hNew = optimalStep[targetIter];<a name="line.736"></a>
<FONT color="green">737</FONT>                        }<a name="line.737"></a>
<FONT color="green">738</FONT>                      }<a name="line.738"></a>
<FONT color="green">739</FONT>                    }<a name="line.739"></a>
<FONT color="green">740</FONT>                    break;<a name="line.740"></a>
<FONT color="green">741</FONT>    <a name="line.741"></a>
<FONT color="green">742</FONT>                  case 0:<a name="line.742"></a>
<FONT color="green">743</FONT>                    if (error &lt;= 1.0) {<a name="line.743"></a>
<FONT color="green">744</FONT>                      // convergence has been reached exactly at targetIter<a name="line.744"></a>
<FONT color="green">745</FONT>                      loop = false;<a name="line.745"></a>
<FONT color="green">746</FONT>                    } else {<a name="line.746"></a>
<FONT color="green">747</FONT>                      // estimate if there is a chance convergence will<a name="line.747"></a>
<FONT color="green">748</FONT>                      // be reached on next iteration, using the<a name="line.748"></a>
<FONT color="green">749</FONT>                      // asymptotic evolution of error<a name="line.749"></a>
<FONT color="green">750</FONT>                      final double ratio = ((double) sequence[k+1]) / sequence[0];<a name="line.750"></a>
<FONT color="green">751</FONT>                      if (error &gt; ratio * ratio) {<a name="line.751"></a>
<FONT color="green">752</FONT>                        // we don't expect to converge on next iteration<a name="line.752"></a>
<FONT color="green">753</FONT>                        // we reject the step immediately<a name="line.753"></a>
<FONT color="green">754</FONT>                        reject = true;<a name="line.754"></a>
<FONT color="green">755</FONT>                        loop = false;<a name="line.755"></a>
<FONT color="green">756</FONT>                        if ((targetIter &gt; 1) &amp;&amp;<a name="line.756"></a>
<FONT color="green">757</FONT>                            (costPerTimeUnit[targetIter-1] &lt;<a name="line.757"></a>
<FONT color="green">758</FONT>                             orderControl1 * costPerTimeUnit[targetIter])) {<a name="line.758"></a>
<FONT color="green">759</FONT>                          --targetIter;<a name="line.759"></a>
<FONT color="green">760</FONT>                        }<a name="line.760"></a>
<FONT color="green">761</FONT>                        hNew = optimalStep[targetIter];<a name="line.761"></a>
<FONT color="green">762</FONT>                      }<a name="line.762"></a>
<FONT color="green">763</FONT>                    }<a name="line.763"></a>
<FONT color="green">764</FONT>                    break;<a name="line.764"></a>
<FONT color="green">765</FONT>    <a name="line.765"></a>
<FONT color="green">766</FONT>                  case 1 :<a name="line.766"></a>
<FONT color="green">767</FONT>                    if (error &gt; 1.0) {<a name="line.767"></a>
<FONT color="green">768</FONT>                      reject = true;<a name="line.768"></a>
<FONT color="green">769</FONT>                      if ((targetIter &gt; 1) &amp;&amp;<a name="line.769"></a>
<FONT color="green">770</FONT>                          (costPerTimeUnit[targetIter-1] &lt;<a name="line.770"></a>
<FONT color="green">771</FONT>                           orderControl1 * costPerTimeUnit[targetIter])) {<a name="line.771"></a>
<FONT color="green">772</FONT>                        --targetIter;<a name="line.772"></a>
<FONT color="green">773</FONT>                      }<a name="line.773"></a>
<FONT color="green">774</FONT>                      hNew = optimalStep[targetIter];<a name="line.774"></a>
<FONT color="green">775</FONT>                    }<a name="line.775"></a>
<FONT color="green">776</FONT>                    loop = false;<a name="line.776"></a>
<FONT color="green">777</FONT>                    break;<a name="line.777"></a>
<FONT color="green">778</FONT>    <a name="line.778"></a>
<FONT color="green">779</FONT>                  default :<a name="line.779"></a>
<FONT color="green">780</FONT>                    if ((firstTime || isLastStep) &amp;&amp; (error &lt;= 1.0)) {<a name="line.780"></a>
<FONT color="green">781</FONT>                      loop = false;<a name="line.781"></a>
<FONT color="green">782</FONT>                    }<a name="line.782"></a>
<FONT color="green">783</FONT>                    break;<a name="line.783"></a>
<FONT color="green">784</FONT>    <a name="line.784"></a>
<FONT color="green">785</FONT>                  }<a name="line.785"></a>
<FONT color="green">786</FONT>    <a name="line.786"></a>
<FONT color="green">787</FONT>                }<a name="line.787"></a>
<FONT color="green">788</FONT>              }<a name="line.788"></a>
<FONT color="green">789</FONT>            }<a name="line.789"></a>
<FONT color="green">790</FONT>          }<a name="line.790"></a>
<FONT color="green">791</FONT>    <a name="line.791"></a>
<FONT color="green">792</FONT>          if (! reject) {<a name="line.792"></a>
<FONT color="green">793</FONT>              // derivatives at end of step<a name="line.793"></a>
<FONT color="green">794</FONT>              computeDerivatives(stepStart + stepSize, y1, yDot1);<a name="line.794"></a>
<FONT color="green">795</FONT>          }<a name="line.795"></a>
<FONT color="green">796</FONT>    <a name="line.796"></a>
<FONT color="green">797</FONT>          // dense output handling<a name="line.797"></a>
<FONT color="green">798</FONT>          double hInt = getMaxStep();<a name="line.798"></a>
<FONT color="green">799</FONT>          if (! reject) {<a name="line.799"></a>
<FONT color="green">800</FONT>    <a name="line.800"></a>
<FONT color="green">801</FONT>            // extrapolate state at middle point of the step<a name="line.801"></a>
<FONT color="green">802</FONT>            for (int j = 1; j &lt;= k; ++j) {<a name="line.802"></a>
<FONT color="green">803</FONT>              extrapolate(0, j, diagonal, yMidDots[0]);<a name="line.803"></a>
<FONT color="green">804</FONT>            }<a name="line.804"></a>
<FONT color="green">805</FONT>    <a name="line.805"></a>
<FONT color="green">806</FONT>            final int mu = 2 * k - mudif + 3;<a name="line.806"></a>
<FONT color="green">807</FONT>    <a name="line.807"></a>
<FONT color="green">808</FONT>            for (int l = 0; l &lt; mu; ++l) {<a name="line.808"></a>
<FONT color="green">809</FONT>    <a name="line.809"></a>
<FONT color="green">810</FONT>              // derivative at middle point of the step<a name="line.810"></a>
<FONT color="green">811</FONT>              final int l2 = l / 2;<a name="line.811"></a>
<FONT color="green">812</FONT>              double factor = FastMath.pow(0.5 * sequence[l2], l);<a name="line.812"></a>
<FONT color="green">813</FONT>              int middleIndex = fk[l2].length / 2;<a name="line.813"></a>
<FONT color="green">814</FONT>              for (int i = 0; i &lt; y0.length; ++i) {<a name="line.814"></a>
<FONT color="green">815</FONT>                yMidDots[l+1][i] = factor * fk[l2][middleIndex + l][i];<a name="line.815"></a>
<FONT color="green">816</FONT>              }<a name="line.816"></a>
<FONT color="green">817</FONT>              for (int j = 1; j &lt;= k - l2; ++j) {<a name="line.817"></a>
<FONT color="green">818</FONT>                factor = FastMath.pow(0.5 * sequence[j + l2], l);<a name="line.818"></a>
<FONT color="green">819</FONT>                middleIndex = fk[l2+j].length / 2;<a name="line.819"></a>
<FONT color="green">820</FONT>                for (int i = 0; i &lt; y0.length; ++i) {<a name="line.820"></a>
<FONT color="green">821</FONT>                  diagonal[j-1][i] = factor * fk[l2+j][middleIndex+l][i];<a name="line.821"></a>
<FONT color="green">822</FONT>                }<a name="line.822"></a>
<FONT color="green">823</FONT>                extrapolate(l2, j, diagonal, yMidDots[l+1]);<a name="line.823"></a>
<FONT color="green">824</FONT>              }<a name="line.824"></a>
<FONT color="green">825</FONT>              for (int i = 0; i &lt; y0.length; ++i) {<a name="line.825"></a>
<FONT color="green">826</FONT>                yMidDots[l+1][i] *= stepSize;<a name="line.826"></a>
<FONT color="green">827</FONT>              }<a name="line.827"></a>
<FONT color="green">828</FONT>    <a name="line.828"></a>
<FONT color="green">829</FONT>              // compute centered differences to evaluate next derivatives<a name="line.829"></a>
<FONT color="green">830</FONT>              for (int j = (l + 1) / 2; j &lt;= k; ++j) {<a name="line.830"></a>
<FONT color="green">831</FONT>                for (int m = fk[j].length - 1; m &gt;= 2 * (l + 1); --m) {<a name="line.831"></a>
<FONT color="green">832</FONT>                  for (int i = 0; i &lt; y0.length; ++i) {<a name="line.832"></a>
<FONT color="green">833</FONT>                    fk[j][m][i] -= fk[j][m-2][i];<a name="line.833"></a>
<FONT color="green">834</FONT>                  }<a name="line.834"></a>
<FONT color="green">835</FONT>                }<a name="line.835"></a>
<FONT color="green">836</FONT>              }<a name="line.836"></a>
<FONT color="green">837</FONT>    <a name="line.837"></a>
<FONT color="green">838</FONT>            }<a name="line.838"></a>
<FONT color="green">839</FONT>    <a name="line.839"></a>
<FONT color="green">840</FONT>            if (mu &gt;= 0) {<a name="line.840"></a>
<FONT color="green">841</FONT>    <a name="line.841"></a>
<FONT color="green">842</FONT>              // estimate the dense output coefficients<a name="line.842"></a>
<FONT color="green">843</FONT>              final GraggBulirschStoerStepInterpolator gbsInterpolator<a name="line.843"></a>
<FONT color="green">844</FONT>                = (GraggBulirschStoerStepInterpolator) interpolator;<a name="line.844"></a>
<FONT color="green">845</FONT>              gbsInterpolator.computeCoefficients(mu, stepSize);<a name="line.845"></a>
<FONT color="green">846</FONT>    <a name="line.846"></a>
<FONT color="green">847</FONT>              if (useInterpolationError) {<a name="line.847"></a>
<FONT color="green">848</FONT>                // use the interpolation error to limit stepsize<a name="line.848"></a>
<FONT color="green">849</FONT>                final double interpError = gbsInterpolator.estimateError(scale);<a name="line.849"></a>
<FONT color="green">850</FONT>                hInt = FastMath.abs(stepSize / FastMath.max(FastMath.pow(interpError, 1.0 / (mu+4)),<a name="line.850"></a>
<FONT color="green">851</FONT>                                                    0.01));<a name="line.851"></a>
<FONT color="green">852</FONT>                if (interpError &gt; 10.0) {<a name="line.852"></a>
<FONT color="green">853</FONT>                  hNew = hInt;<a name="line.853"></a>
<FONT color="green">854</FONT>                  reject = true;<a name="line.854"></a>
<FONT color="green">855</FONT>                }<a name="line.855"></a>
<FONT color="green">856</FONT>              }<a name="line.856"></a>
<FONT color="green">857</FONT>    <a name="line.857"></a>
<FONT color="green">858</FONT>            }<a name="line.858"></a>
<FONT color="green">859</FONT>    <a name="line.859"></a>
<FONT color="green">860</FONT>          }<a name="line.860"></a>
<FONT color="green">861</FONT>    <a name="line.861"></a>
<FONT color="green">862</FONT>          if (! reject) {<a name="line.862"></a>
<FONT color="green">863</FONT>    <a name="line.863"></a>
<FONT color="green">864</FONT>            // Discrete events handling<a name="line.864"></a>
<FONT color="green">865</FONT>            interpolator.storeTime(stepStart + stepSize);<a name="line.865"></a>
<FONT color="green">866</FONT>            stepStart = acceptStep(interpolator, y1, yDot1, t);<a name="line.866"></a>
<FONT color="green">867</FONT>    <a name="line.867"></a>
<FONT color="green">868</FONT>            // prepare next step<a name="line.868"></a>
<FONT color="green">869</FONT>            interpolator.storeTime(stepStart);<a name="line.869"></a>
<FONT color="green">870</FONT>            System.arraycopy(y1, 0, y, 0, y0.length);<a name="line.870"></a>
<FONT color="green">871</FONT>            System.arraycopy(yDot1, 0, yDot0, 0, y0.length);<a name="line.871"></a>
<FONT color="green">872</FONT>            firstStepAlreadyComputed = true;<a name="line.872"></a>
<FONT color="green">873</FONT>    <a name="line.873"></a>
<FONT color="green">874</FONT>            int optimalIter;<a name="line.874"></a>
<FONT color="green">875</FONT>            if (k == 1) {<a name="line.875"></a>
<FONT color="green">876</FONT>              optimalIter = 2;<a name="line.876"></a>
<FONT color="green">877</FONT>              if (previousRejected) {<a name="line.877"></a>
<FONT color="green">878</FONT>                optimalIter = 1;<a name="line.878"></a>
<FONT color="green">879</FONT>              }<a name="line.879"></a>
<FONT color="green">880</FONT>            } else if (k &lt;= targetIter) {<a name="line.880"></a>
<FONT color="green">881</FONT>              optimalIter = k;<a name="line.881"></a>
<FONT color="green">882</FONT>              if (costPerTimeUnit[k-1] &lt; orderControl1 * costPerTimeUnit[k]) {<a name="line.882"></a>
<FONT color="green">883</FONT>                optimalIter = k-1;<a name="line.883"></a>
<FONT color="green">884</FONT>              } else if (costPerTimeUnit[k] &lt; orderControl2 * costPerTimeUnit[k-1]) {<a name="line.884"></a>
<FONT color="green">885</FONT>                optimalIter = FastMath.min(k+1, sequence.length - 2);<a name="line.885"></a>
<FONT color="green">886</FONT>              }<a name="line.886"></a>
<FONT color="green">887</FONT>            } else {<a name="line.887"></a>
<FONT color="green">888</FONT>              optimalIter = k - 1;<a name="line.888"></a>
<FONT color="green">889</FONT>              if ((k &gt; 2) &amp;&amp;<a name="line.889"></a>
<FONT color="green">890</FONT>                  (costPerTimeUnit[k-2] &lt; orderControl1 * costPerTimeUnit[k-1])) {<a name="line.890"></a>
<FONT color="green">891</FONT>                optimalIter = k - 2;<a name="line.891"></a>
<FONT color="green">892</FONT>              }<a name="line.892"></a>
<FONT color="green">893</FONT>              if (costPerTimeUnit[k] &lt; orderControl2 * costPerTimeUnit[optimalIter]) {<a name="line.893"></a>
<FONT color="green">894</FONT>                optimalIter = FastMath.min(k, sequence.length - 2);<a name="line.894"></a>
<FONT color="green">895</FONT>              }<a name="line.895"></a>
<FONT color="green">896</FONT>            }<a name="line.896"></a>
<FONT color="green">897</FONT>    <a name="line.897"></a>
<FONT color="green">898</FONT>            if (previousRejected) {<a name="line.898"></a>
<FONT color="green">899</FONT>              // after a rejected step neither order nor stepsize<a name="line.899"></a>
<FONT color="green">900</FONT>              // should increase<a name="line.900"></a>
<FONT color="green">901</FONT>              targetIter = FastMath.min(optimalIter, k);<a name="line.901"></a>
<FONT color="green">902</FONT>              hNew = FastMath.min(FastMath.abs(stepSize), optimalStep[targetIter]);<a name="line.902"></a>
<FONT color="green">903</FONT>            } else {<a name="line.903"></a>
<FONT color="green">904</FONT>              // stepsize control<a name="line.904"></a>
<FONT color="green">905</FONT>              if (optimalIter &lt;= k) {<a name="line.905"></a>
<FONT color="green">906</FONT>                hNew = optimalStep[optimalIter];<a name="line.906"></a>
<FONT color="green">907</FONT>              } else {<a name="line.907"></a>
<FONT color="green">908</FONT>                if ((k &lt; targetIter) &amp;&amp;<a name="line.908"></a>
<FONT color="green">909</FONT>                    (costPerTimeUnit[k] &lt; orderControl2 * costPerTimeUnit[k-1])) {<a name="line.909"></a>
<FONT color="green">910</FONT>                  hNew = filterStep(optimalStep[k] * costPerStep[optimalIter+1] / costPerStep[k],<a name="line.910"></a>
<FONT color="green">911</FONT>                                   forward, false);<a name="line.911"></a>
<FONT color="green">912</FONT>                } else {<a name="line.912"></a>
<FONT color="green">913</FONT>                  hNew = filterStep(optimalStep[k] * costPerStep[optimalIter] / costPerStep[k],<a name="line.913"></a>
<FONT color="green">914</FONT>                                    forward, false);<a name="line.914"></a>
<FONT color="green">915</FONT>                }<a name="line.915"></a>
<FONT color="green">916</FONT>              }<a name="line.916"></a>
<FONT color="green">917</FONT>    <a name="line.917"></a>
<FONT color="green">918</FONT>              targetIter = optimalIter;<a name="line.918"></a>
<FONT color="green">919</FONT>    <a name="line.919"></a>
<FONT color="green">920</FONT>            }<a name="line.920"></a>
<FONT color="green">921</FONT>    <a name="line.921"></a>
<FONT color="green">922</FONT>            newStep = true;<a name="line.922"></a>
<FONT color="green">923</FONT>    <a name="line.923"></a>
<FONT color="green">924</FONT>          }<a name="line.924"></a>
<FONT color="green">925</FONT>    <a name="line.925"></a>
<FONT color="green">926</FONT>          hNew = FastMath.min(hNew, hInt);<a name="line.926"></a>
<FONT color="green">927</FONT>          if (! forward) {<a name="line.927"></a>
<FONT color="green">928</FONT>            hNew = -hNew;<a name="line.928"></a>
<FONT color="green">929</FONT>          }<a name="line.929"></a>
<FONT color="green">930</FONT>    <a name="line.930"></a>
<FONT color="green">931</FONT>          firstTime = false;<a name="line.931"></a>
<FONT color="green">932</FONT>    <a name="line.932"></a>
<FONT color="green">933</FONT>          if (reject) {<a name="line.933"></a>
<FONT color="green">934</FONT>            isLastStep = false;<a name="line.934"></a>
<FONT color="green">935</FONT>            previousRejected = true;<a name="line.935"></a>
<FONT color="green">936</FONT>          } else {<a name="line.936"></a>
<FONT color="green">937</FONT>            previousRejected = false;<a name="line.937"></a>
<FONT color="green">938</FONT>          }<a name="line.938"></a>
<FONT color="green">939</FONT>    <a name="line.939"></a>
<FONT color="green">940</FONT>        } while (!isLastStep);<a name="line.940"></a>
<FONT color="green">941</FONT>    <a name="line.941"></a>
<FONT color="green">942</FONT>        // dispatch results<a name="line.942"></a>
<FONT color="green">943</FONT>        equations.setTime(stepStart);<a name="line.943"></a>
<FONT color="green">944</FONT>        equations.setCompleteState(y);<a name="line.944"></a>
<FONT color="green">945</FONT>    <a name="line.945"></a>
<FONT color="green">946</FONT>        resetInternalState();<a name="line.946"></a>
<FONT color="green">947</FONT>    <a name="line.947"></a>
<FONT color="green">948</FONT>      }<a name="line.948"></a>
<FONT color="green">949</FONT>    <a name="line.949"></a>
<FONT color="green">950</FONT>    }<a name="line.950"></a>




























































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